A bird is considered "egocentric" if it is fond of itself: if, when called with itself, it responds with itself.
Show that, under the conditions of the previous problem's forest, at least one bird is egocentric.
We have already proved that every bird is fond of at least one other bird, and we know the forest contains a Mockingbird. So, we can assume there exists a bird E that the Mockingbird is fond of.
Because the Mockingbird is fond of E, we know that M(E) evaluates to E. And from the Mockingbird's definition, we also know that M(E) evaluates to E(E). For both to be true, E and E(E) must be the same. Thus, there exists a bird that is egocentric.
M(E); // => E, from behavior of "fondness"
M(E); // => E(E), from definition of M
E === E(E);